Talk:Moment magnitude scale

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1 Notation
2 More prominent: SI or CGS?
3 SI: approximation -> exact???
4 Dimensional analysis
5 Energy example
6 Formulas
7 Energy formula inaccurate above 8.0?
8 Tom Hanks
9 Wretched formulas (units problem, etc.)
10 Just wondering
11 Real world examples please
12 Strange formula
13 Richter Scale Inconsistency?

[edit] Notation

Why is moment magnitude indicated with the letters M_W? What does the W stand for? -- Rod Thompson, Hilo, Hawaii

Good question... I don't immediately find the answer by googling. The notation was probably introduced in Kanamori's 1977 paper in the Journal of Geophysical Research, but I don't have that handy. The origin of notation in the sciences is often rather obscure. Gwimpey 06:14, 24 May 2004

In the equation for seismic moment is a capital omega not, which is equal to spectral amplitude at low frequencies and or equivalently on a broadband displacement seismogram the product of pulse with and amplitude. The lower case symbol for omega closely resembles a w. This was taken from an informal poll of workers that came in on a holiday at a large seismic network. Ref is "An introduction to the theory of seismology" by Bullen and Bolt page 426 and 427. (not my favorite seis book though) Annonymous

Interesting. So should we actually write M_Ω or M_ω? I know that some Microsoft programs convert "ω" into "w" and equivalently "Ω" into "W" when converting from Unicode to a non-Greek 8-bit legacy character set (which makes for interesting reading when having a "4.7 MW resistor" specified in a small circuit :-). In signal processing and physics (see ISO 31-2), ω = 2πf stands for the angular velocity, a measure of frequency that saves you having to write 2π in many formulas related to the Fourier transform. Is that what is used here, i.e. is the quantity meant to be frequency dependent? Markus Kuhn 11:22, 13 Jun 2005 (UTC)

The underlying question is, whether we should copy this rather confusing mix of indices on the magnitude quantity at all, or look instead for an existing more streamlined and systematic presentation and notation in the literature (a good textbook, some formal standard?) and take the notation from there, rather than from the original articles. Looking for some good books worldwide is probably more helpful than googling here. Any suggestions? Markus Kuhn 11:22, 13 Jun 2005 (UTC)

W stands for the "difference in elastic strain energy W before and after an earthquake" in : Kanamori H. (1977). The energy release in great earthquakes. J. Geophys. Res., 82, 2981-2987. This article is the reference paper for moment magnitude where it is defined for the first time. The original formulation links the energy called W in the paper to a new magnitude called by the author M_w. The relation linking the seismic moment to this magnitude, even if it is nowadays a common formula in seismology, is a secondary product in this article. The author gives only the relation between energy W and seismic moment M₀. Thus even if deducing the formula between the seismic moment and the new magnitude is straightforward, the relation is not explicitly written. It is explicitly written (equation 4) in this brief paper : Hanks T. and H. Kanamori (1979). A moment magnitude scale. J. Geophys. Res., 84, 2348-2350. andre 09:57, 14 September 2006 (UTC)

[edit] More prominent: SI or CGS?

Shouldn't SI be more prominent? Do we even need the formula in CGS units? This unnecessarily complicates things. Shameer 01:14, 28 Dec 2004 (UTC)

Presumably, if developed in 1977, the scale may have been developed for cgs units. I'm not certain, but yes, I'd agree that the SI equation should be listed before the cgs equation. --ABQCat 02:28, 28 Dec 2004 (UTC)

-- Why, physicists use so many unit system variants and choose what ever system makes the math the easiest for them. My favorite are God's units or natural units

[edit] SI: approximation -> exact???

Here is the approximation from the article:

$M_W = {2 \over 3}\log_{10} M_{0,\mathrm{SI}} - 6.\,$

This can be changed to the following, which is exact, assuming the "cgs equation" is exact.

$M_W = {2 \over 3}\log_{10} M_{0,\mathrm{SI}} - \left(6.7 - {2 \over 3}\right).\,$

[edit] Dimensional analysis

Here, we are taking the logarithm of a quantity with units, which is forbidden by the dimensional analysis article. Brianjd 06:24, 2004 Dec 29 (UTC)

So you can't do a full dimensional analysis of all this. Sometimes you just have to accept that this is HOW they do it without understanding WHY they do it this way. I do recall a few times in my engineering classes when we needed to take logarithms of quantities with units - the professors told us not to worry and to just bring the units outside the logarithm. --ABQCat 07:47, 29 Dec 2004 (UTC)

I haven't read it fully because my studies are not advanced enough to understand it, but it doesn't seem to mention any exceptions. So it seems that it needs to be changed. Brianjd 07:42, 2005 Jan 11 (UTC)

After taking the logarithm, you have a quantity with units of the type mass×length²/time², from which you have to subtract a dimensionless number. How do you explain that? One could say that the number has the same units, in which case the final result also has those units, so how is it a "scale"?

Maybe it's a really kludgy way to do this, but maybe the equation WORKS if the value of the moment is in the correct units, but for use in the calculation the units are stripped off? That would eliminate logs of units and subtracting dimensionless numbers. Again, I don't know, but it's possible. --ABQCat 23:29, 11 Jan 2005 (UTC)

The old formulas (prior to 12 June 2005) were an outstanding example of how not to use physical quantities in modern scientific writing. I've decided to be bold and replaced them with an equivalent version that follows the ISO 31-0 convention of using division by a unit when it is necessary to convert a physical quantity into a dimensionfree numerical value. This way, each formula becomes independent of the units used to write down the quantities. No more need to have "SI" indices and similar nonsense. I nevertheless left several forms of the expression standing, using both SI and CGS units in the division, for the benefit of people who are not experienced in converting between CGS and SI. It would be nice is someone finally taught the authors of USGS web sites how to use units properly ... Markus Kuhn 12:45, 12 Jun 2005 (UTC)

[edit] Energy example

There was an example which said: sonny For example, M0 = 6,7,8,9 means energies of approximately 1 petajoule (1 PJ = 1015 Joules), 32 petajoules, 1 exajoule (1 EJ = 1018 Joules), 32 exajoules.

I removed it because M0 should increase linearly with energy and Mw was what was probably intended. If I replaced M0 with Mw, the energies didn't match these sources: [1] [2]. Some one else who has more knowledge of this can add it back. Shameer 00:16, 30 Dec 2004 (UTC)

-- At work sometimes I see magnitudes expressed in eqv killo tons of tnt. Maybe we should try it here too, it was a nice representation

Yes, I meant Mw. I changed it, now also taking into account the two conversion factors, as I understand them from the links.--Patrick 11:55, Dec 31, 2004 (UTC)

Seeking support for "The energy is 1/2000 times the moment," I read [3] but remained confused. The "magnitude 6 = 1 megaton TNT" rule in [4] suggests a formula more like

$M_W = {2 \over 3}\log_{10} E_{\mathrm{SI}} - 4.4\,$

--Mgarraha 22:22, Dec 31, 2004 (UTC)

I hope the rephrased section on kt TNT comparisons makes it clear, that neither earthquakes nor underground nuclear weapons tests release more than a tiny fraction of their total converted energy in the form of seismic waves, and that therefore any comparison between the two is only meaningful if you agree on a seismic efficiency coefficient for the nuclear weapon. That of course depends a lot on the design of the test and the test site. Since all conversion formulas are equally useless and misleading, I find sympathy for the established secret convention of telling any naive journalists who insists on a TNT comparision a conventional figure that is based on magnitude 0 being equivalent to 1 kg TNT. That saves the seismologists unnecessary mental arithmetic on the phone when a journalist really does not want to go away without a TNT figure, and everyone is happy. Markus Kuhn 13:19, 12 Jun 2005 (UTC)

[edit] Formulas

see history

I notice that it was changed from the "preferred" formula to another formula. Why? I quote the following from [5]: "Another source of confusion is the form of the formula for converting from scalar moment M0 to moment magnitude, M. The preferred practice is to use M = (log Mo)/1.5-10.7, where Mo is in dyne-cm (dyne-cm=10-7 N-m), the definition given by Hanks and Kanamori in 1979. An alternate form in Hanks and Kanamori’s paper, M=(log M0-16.1)/1.5, is sometimes used, with resulting confusion. These formulae look as if they should yield the same result, but the latter is equivalent to M = (log Mo)/1.5-10.7333. The resulting round-off error occasionally leads to differences of 0.1 in the estimates of moment magnitude released by different groups. All USGS statements of moment magnitude should use M = (log Mo)/1.5-10.7 for converting from scalar moment Mo to moment magnitude." Anonymous

I suggest we keep for the moment the version with parenthesis where the factor 2/3 is not already multiplied into the offset. This form ensures that the SI and the CGS versions remain consistent without rounding errors when written using a fraction-free decimal offset. Otherwise, the final constant would have to change by the ugly offset of 7*(2/3). In that respect, the above quoted USGS policy is a somewhat unfortunate choice. Let's hope that it is already outdated and that they now finally also use SI, like everyone else. Markus Kuhn 13:00, 12 Jun 2005 (UTC)

So what's the evidence against the USGS formula? Is the alternative form a standard anywhere else? To be clear, I'm not concerned about the units here, I'm concerned about the numeric result. ~brad 9 Feb 2006

[edit] Energy formula inaccurate above 8.0?

I read an article by a local Geology professor stating that the energy released by an 8.5 is over 10 times greater than the energy released by an 8.0.

According to the energy formulas in the article, the energy should only be 5.62 times greater.

I emailed the professor, and she said the simple formula fails for "very large" earthquakes due to:

a non linear increase in frictional heat release
free oscillations generated
impacts on rotation
permanent deformation

This is all over my head. Is it worth mentioning in the article that the energy formula fails for large earthquakes?

Maybe. I'm not sure that I understand exactly what she meant. I think it depends which energy she is talking about. The total energy release formula is $\mathcal{E}_r = - (\mathcal{E}_e + \mathcal{E}_g + \mathcal{E}_k)$ where $\mathcal{E}_e$ , $\mathcal{E}_g$ , and $\mathcal{E}_k$ represent elastic, gravitational, and kinetic energy. In addition, there is the concept of seismic energy, which is the total released energy minus the energy dissipated by frictional heating of the fault. I am pretty sure that the total released energy is still estimated correctly by the moment. However, the partitioning of the energy may change in the ways the professor noted. When talking about energy here, it's important to know exactly what energy is being referred to. Note: The text I consulted is Theoretical global seismology by Dahlen and Tromp (1998). Gwimpey 18:49, Jan 19, 2005 (UTC)

[edit] Tom Hanks

Tom Hanks is an actor (real name Thomas Jeffrey Hanks) This article points to an article about him, but i think this Tom Hanks is a different person

[edit] Wretched formulas (units problem, etc.)

The "Energy" section really sucks: it is both redundant and confusing. For starters, Log(x) only makes sense if x is dimensionless. These formulas should be recast in the form Log(x/x0), where x and x0 have the same dimensions. Give x0 in several different units, and get rid of all but one of the nearly identical equations. Also, give the inverted version of the equation to give energy in terms of moment magnitude -- the more useful direction for the calculation. I'm just passing through, but it would be nice if someone would redo this section from scratch.

I've fixed the unit mess and cleaned up the wretched energy section. I wanted to preserve the underlying information in the latter, so I split it up into separate sections on the energy magnitude and on comparing earthquake magnitudes with TNT-expressed underground nuclear detonations. If people want to keep things short, I'd be happy to agree that both sections could be moved to other articles, with appropriate cross references. If people stopped the silly and utterly meaningless practice of comparing earthquakes with nuclear detonations, that would be even better! Markus Kuhn 13:08, 12 Jun 2005 (UTC)

[edit] Just wondering

what is the difference from a 4.0 on the richter scale to a magnitude of 5.0?

The article explains this very clearly already. Markus Kuhn 23:51, 9 December 2005 (UTC)

[edit] Real world examples please

Could a table be drawn up to show examples at each part of the scale like the Richter magnitude scale article does? The Basel earthquake says it had a mwm of 6.2, and I have no idea what that means in terms of power. The artcle needs some more for the layman, as right now it's all technical jargon to me.--SeizureDog 14:04, 5 January 2007 (UTC)

I concur. And I don't see anywhere where the comparison with Richter is explained, let alone "very clearly"! How about a small chart giving Richter and Mms values (assuming they are always the same for a given quake, which I can't tell from this convoluted article) and something like destruction or energy released.

[edit] Strange formula

I have noticed that after the main formula the symbols N and m are not explained. Reading previous discussions, I think they stand for Newton and meter to make M₀ dimensionless. It doesn't really make sense, since they look like other parameters with their own value, in any case their meaning should be clear from the context and it's not. I would suggest a notation like this:

$M_\mathrm{w} = {2 \over 3}\left(\log_{10} | M_0 | - 9.1\right)$

where $| M 0 |$ is the dimensionless module of the seismic moment

About another previous discussion, I absolutely agree that in physics it is not correct to calculate the logarithm of any number that is not dimensionless, but in engineering it is quite common to represent dimension-ful functions with a very wide range using logarithmic scales. For example, the Bode plot of a voltage-to-current amplifier is the plot of a dimension-ful number [A/V] on a logarithmic scale. There is no problem in taking the logarithm of a dimension-ful number, as long as it's only for measuring or plotting sake. I can agree that the best scales use a reference to make the argument of the logarithm dimensionless (e.g. dB spl: Tom Hanks and Hiroo Kanamori didn't make their scale properly from this point of view. We could fix it writing like:

$M_\mathrm{w} = {2 \over 3}\left(\log_{10} \frac{M_0}{M_r} - 9.1\right)$

where $| M 0 |$ is the dimensionless module of the seismic moment and $M r$ is the reference value of 1 Nm

but it would be original work, I guess (even if it's definitely more rigorous then the original) Alessio Damato ^(Talk) 10:40, 17 August 2007 (UTC)

I think the formula is currently expressed very well and should not be changed as you suggest. It currently follows the stylistic guidelines given in various International Standards related to scientific notation (e.g., ISO 31-0, SI Brochure, etc.), which specify that variable quantities are distinguished typographically from units and other constants by use of italic characters. ISO 31-0 also specifies that a quantity is always a product of a number and a unit, and if you need a dimensionless number, you can simply access that by dividing the quantity through the unit in which you want the number to express the quantity. The current formula also uses the well-understood international standard symbols for the units used in the correct font. All these are world-wide very well-established conventions in scientific writing, that are globally taught in most secondary-school physics classes. I personally find them pretty convenient, logical, and easy to understand. On the other hand, I find your first alternative formula confusing, as it suggests calculating the logarithm of an energy quantity, which physically makes no sense. Your second formula is identical to the current one after the substitution M_r = 1 Nm, and therefore the current formula should be just as good as your second alternative. It simply avoids the unnecessary introduction of another, redundant quantity M_r. I suspect it all boils down to that you might not have been familiar with the (pretty common) typographic convention that units of measurements are not typeset in italics (NIST SP 811, etc.). Markus Kuhn 12:23, 18 August 2007 (UTC)

well, as you like, but I'll point out clearly in the description that they are not parameters with their own value. Alessio Damato ^(Talk) 15:06, 18 August 2007 (UTC)

Markus, I don't think the confusion was with the font. The confusion was with the notion of dividing by a unit. The concept that "if you need a dimensionless number, you can simply access that by dividing the quantity through the unit in which you want the number to express the quantity" is, I believe, not widely appreciated by educated adults in the U.S. It does make sense when you think about it, however. I have added a sentence explaining the notation. Mark Foskey (talk) 02:48, 14 May 2008 (UTC)

I see. I would have expected the notion to be pretty familiar and clear to most people in Europe who have enjoyed some form of secondary-school education in physics. But I admit that I do notice occasionally that some American authors do things with units that I would consider rather odd and cumbersome, possibly because they have not grown up with thinking of them just as factors that can be divided or multiplied like any other factor, or because an algebraic way of using units is not commonly taught there. I was taught that writing formulas like

F = m · a, where F is in newtons, m is in kilos and a is in m/s²

is bad style, as the units should always sort themselves out algebraically on their own in physical formulas. One should therefore never have to explicitly say which variable is measured in which unit, as they are just quantities that work no matter what the unit is. Only in ad-hoc scales that require logarithms, it actually becomes necessary to explicitly divide through a particular unit, as the formulas in this article do. Is the algebraic use of physical units only widely taught in countries that use mostly SI units and can we therefore not just simply assume familiarity with it in Wikipedia articles about scientific topics? Markus Kuhn (talk) 14:08, 14 May 2008 (UTC)

[edit] Richter Scale Inconsistency?

The article about the Richter Scale has the following:

The energy release of an earthquake scales with the 3⁄2 power of the shaking amplitude, and thus a difference in magnitude of 1.0 is equivalent to a factor of 31.6 in the energy released; a difference of magnitude of 2.0 is equivalent to a factor of 1000 in the energy released.

This article, when mentioning the Richter Scale has the following:

...the Richter Scale, which has a 10¹ = 10 times energy increase for a 1 step increase, and 10² = 100 times energy increase for a 2 step increase. Instead, an increase of 2 steps corresponds to a 10³ = 1000 times increase in energy.

If I assume the information about the Richter Scale in the Richter Scale article is accurate, it appears an editor of this article has confused amplitude with energy when referring to the Richter Scale. SlowJog (talk) 16:23, 13 May 2008 (UTC)

I found a USGS page that discusses the Richter magnitude scale and specifically states, "each whole number step in the magnitude scale corresponds to the release of about 31 times more energy than the amount associated with the preceding whole number value." This page was part of the external links on the Richter magnitude scale page, I changed it to a citation.

Another USGS page states, "All of the currently used methods for measuring earthquake magnitude (ML, duration magnitude mD, surface-wave magnitude MS, teleseismic body-wave magnitude mb, moment magnitude M, etc.) yield results that are consistent with ML. In fact, most modern methods for measuring magnitude were designed to be consistent with the Richter scale." Added this as an external link on the Richter magnitude scale page. Gblandst (talk) 17:43, 13 May 2008 (UTC)